Question

suppose that a certain college class contains 61 students. of these, 35 are juniors, 30 are economics majors, and 6 are neither. a student is selected at random from the class.

(a) what is the probability that the student is both a junior and an economics major?
(b) given that the student selected is a economics major, what is the probability that he is also an junior?

write your responses as fractions. (if necessary, consult a list of formulas.)

Explanation:

Define the given sets and values

Using the Probability of Events knowledge point

$$
LATEXBLOCK0
$$

Find the union of the two sets

Using the Probability of Events knowledge point

$$
LATEXBLOCK1
$$

Find the intersection of the two sets

Using the Addition Rule of Probability knowledge point

$$
LATEXBLOCK2
$$

Calculate the probability of both events occurring

Using the Probability of Events knowledge point

$$ P(J \cap E) = \frac{N(J \cap E)}{N(S)} = \frac{10}{61} $$

Calculate the conditional probability

Using the Conditional Probability knowledge point

$$ P(J \mid E) = \frac{N(J \cap E)}{N(E)} = \frac{10}{30} = \frac{1}{3} $$

Answer:

Suppose that a certain college class contains 61 students. Of these, 35 are juniors, 30 are economics majors, and 6 are neither. A student is selected at random from the class.

(a) What is the probability that the student is both a junior and an economics major? <blank>\(\frac{10}{61}\)</blank>

(b) Given that the student selected is a economics major, what is the probability that he is also an junior? <blank>\(\frac{1}{3}\)</blank>